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arXiv · 1211.1353

On the existence of large degree Galois representations for fields of small discriminant

Jeremy Rouse·Frank Thorne
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Abstract

Let $L/K$ be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of ${\rm Gal}(L/K)$, the sharper of which is conditional on the Artin Conjecture and the Generalized Riemann Hypothesis. Our bound is nontrivial when $[K : \mathbb{Q}]$ is small and $L$ has small root discriminant, and might be summarized as saying that such fields can't be "too abelian."

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Jeremy Rouse, Frank Thorne. 2012-11-06. On the existence of large degree Galois representations for fields of small discriminant. https://doi.org/10.2140/pjm.2014.271.243

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